Đặt \(sinx=t\in\left[-1;1\right]\)
\(\Rightarrow t^2+2\left(m+1\right)t-3m^2+6m=0\)
\(\Leftrightarrow t^2+2mt-3m^2+2t+6m=0\)
\(\Leftrightarrow\left(t-m\right)\left(t+3m\right)+2\left(t+3m\right)=0\)
\(\Leftrightarrow\left(t+3m\right)\left(t-m+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}t=-3m\\t=m-2\end{matrix}\right.\)
Pt có nghiệm khi: \(\left[{}\begin{matrix}-1\le3m\le1\\-1\le m-2\le1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}-\dfrac{1}{3}\le m\le\dfrac{1}{3}\\1\le m\le3\end{matrix}\right.\)
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